Question: Rewrite as a simplified fraction. ${0.\overline{51} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 51.5151...\\ 1x &= 0.5151...\end{align*}}$ Subtracting the two equations, we have: ${99x = 51}$ ${x = \dfrac{51}{99}} $ ${x = \dfrac{17}{33}} $